Circular Motion Lecture
Tommie
One of the simplest of periodic motions is uniform circular motion. By shadow projecting both uniform circular motion and oscillatory simple harmonic motion onto a screen, one can show that these two seemingly different kinds of motion are actually identical.
A 8 cm diameter plastic ball mounted near the edge of a 46 cm diameter disk undergoes uniform circular motion. The disk, oriented vertically, is driven by a 57 RPM motor.1 A large iron weight (14.87 kg), suspended from a stiff spring, is the simple harmonic oscillator. The spring/weight combination has been carefully chosen so that its period of motion is almost identical to the motor.
Because the frequencies of the two systems are not perfectly identical, the shadows start to noticeably get out of phase with each other after a dozen or so oscillations. The demonstration can be stopped before that happens.
Figure 61:Polar coordinates.Let us define two unit vectors, and . Incidentally,a unit vector simply a vector whose length is unity. As shown in Fig. 61, the radialunit vector always points from the origin to the instantaneous position of the object.Moreover, the tangential unit vector is always normalto , in the direction of increasing . The position vector of the object can be written
(270)
Figure 62:Representation of a complex number in the complex plane.Consider the complex number , where is real.A famous result in complex analysis--known as de Moivre's theorem--allows usto split this number into its real and imaginary components:
(276)
Figure 63:Representation of the unit vectors and in the complex plane.Consider an object executing non-uniform circular motion in the complex plane. By analogywith Eq. (270), we can represent the instantaneous position vector ofthis object via the complex number
(280)
Let us now consider the commonly occurring special case in which an object executes a circularorbit at fixed radius, but varying angular velocity. Since the radius is fixed, it followsthat . According to Eqs. (282) and (283), the radialvelocity of the object is zero, and the tangential velocity takes the form
(287)
This research aimed to explore the comparative impact of Process Oriented Guided Inquiry Learning (POGIL)-based instruction and traditional lecture-based instruction on the academic performance of Grade 12 students in the context of the circular motion unit. Employing a quasi-experimental pretest-posttest design, the study assessed students' cognitive outcomes in terms of Knowing, Applying, and Reasoning (KAR). A total of 110 participants were involved, with 54 assigned to the treatment group (25 girls and 29 boys) and 56 to the control group (27 girls and 29 boys). The treatment group received instruction on circular motion through POGIL, while the control group underwent lecture-based instruction. The results revealed statistically significant differences in circular motion performance between the control and treatment groups, with the latter exhibiting superior outcomes. This suggests that POGIL-based instruction positively influences students' understanding of circular motion, emphasizing its efficacy in enhancing learning outcomes in comparison to traditional lecture-based methods.
Uniform Circular Motion: Lecture Notes (Circular Motion) - we will be studying the simplest type of circular motion; uniform circular motion, which is motion in a circle at constant speed - for example, if you have a car that travels around a perfectly circular track so that at every instant the speedometer reads 60 miles/hour you are in uniform circular motion Linear Speed: - in order to determine if an object in circular motion is moving at constant speed we can apply the same test that we used earlier to decide whether or not an object was traveling in a straight line with constant average speed - we will measure the distances traveled along the circumference in given time intervals and determine if the ratios of d t are equal - for circles, it is easy to use one complete circumference of the circle as the distance traveled - if we know the radius r, this distance C is given by the formula C 2 r - the time required for an object to complete one revolution around the circle is the period, T - the number of revolutions completed by an object in a unit of time is called the frequency, f
This study investigates the impact of lecture-based instruction and process-oriented guided inquiry learning (POGIL)-based instruction on the self-efficacy and performance of Grade 12 students. The researchers used a quasi-experimental, pretest-posttest design to compare the effects of POGIL-based instruction to lecture-based instruction, as measured by three cognitive outcomes: knowing, applying, and reasoning (KAR)." self-efficacy as measured by physics learning variables", "understanding of physics", and "willingness to learn". The study included 110 participants (54 in the treatment group and 56 in the control group) and was conducted in two government high schools in Alain, one for boys and one for girls. POGIL-based instruction was used to teach a circular motion unit in physics to the treatment group, while lecture-based instruction was used for the control group. The findings show that POGIL-based instruction had a statistically significant positive impact on science performance and self-efficacy when compared to lecture-based instruction. Furthermore, after the intervention, there was a positive correlation between participants' KAR test performance and their self-efficacy toward scientific inquiry. The study recommends a shift toward POGIL-based instruction to improve students' performance and self-efficacy and suggests that future research should include a broader range of schools, teachers, and advisors.
This third course serves as an introduction to the physics of rotational motion and gravitation. Learners will gain experience in solving physics problems with tools such as graphical analysis, algebra, vector analysis, and calculus. This third course covers Rotational motion, Angular Momentum, and Gravitation.
Upon completion, learners will understand how mathematical laws and conservation principles describe the motions and interactions of objects around us. Each of the modules contain reading links to a free textbook, complete video lectures, conceptual quizzes, and a set of homework problems. Once the modules are completed, the course ends with an exam. This comprehensive course is similar in detail and rigor to those taught on-campus at Rice. It will thoroughly prepare learners for their upcoming introductory physics courses or more advanced courses in physics.
Jason Hafner earned his Ph.D. from Rice University in 1998 under Richard Smalley for work on carbon nanotubes, and pursued postdoctoral studies at Harvard University. He returned to Rice in 2001 to join the faculty where his lab studies nanophotonics and interfacial biology. Hafner was named a Beckman Young Investigator in 2002, and won the Norman Hackerman Award for Chemical Research from the Welch Foundation in 2011. He is currently a Professor of Physics and Astronomy and of Chemistry.
This is a pre-calculus introductory physics course for pre-medical, pre-dental, pre-chiropractic and pre-physical therapy students and students working toward a degree. Topic of study is mechanics, and includes statics, forces and motion, energy, collisions, circular motion and rotation. This course meets college transfer, Oregon Block Transfer and program requirements as listed above.
After completion of this course, students will
1) Apply knowledge of linear motion, forces, energy, and circular motion to explain natural physical processes and related technological advances.
2) Use an understanding of algebraic mathematics along with physical principles to effectively solve problems encountered in everyday life, further study in science, and in the professional world.
3) Design experiments and acquire data in order to explore physical principles, effectively communicate results, and critically evaluate related scientific studies.
4) Assess the contributions of physics to our evolving understanding of global change and sustainability while placing the development of physics in its historical and cultural context.
Principles and techniques are presented through lectures and class demonstrations. Students must register for lecture and one laboratory. Laboratory work will be performed in order to clarify certain facts in the lecture material.
At the beginning of the course, the instructor will provide a syllabus that details the methods used to evaluate student progress and the criteria for assigning a course grade. The methods may include one or more of the following tools: examinations, quizzes, homework assignments, laboratory reports, research papers, small group problem solving of questions arising from application of course concepts and concerns to actual experience, oral presentations, or maintenance of a personal lab manual. Specific evaluation procedures will be given in class. In general, grading will be based on accumulated points from homework assignments, tests, a final exam, and labs.
a. vectors and scalars
b. components of vectors (This includes a brief introduction to sine, cosine, tangent and their inverses, since these are not covered in the math prerequisite for this course.)
c. graphical solutions to vector problems
d. analytical solutions to vector problems
2.1 Distinguish speed from velocity and solve appropriate problems involving these concepts.
2.2 Define uniform acceleration.
2.3 State the equations for uniformly accelerated motion and understand their derivation. Solve problems involving these equations.
2.4 Explain the special conditions that define "free fall" as a special case of uniformly accelerated motion.
2.5 Introduce the concept of projectile motion and solve appropriate problems. Emphasis is put on x-y independence.